Respuesta :


[tex] \sqrt{17 {}^{2} { - 8}^{2} } = 15 \\ 21 - 15 = 6 \\ \sqrt{8 { }^{2} } + \sqrt{6 } {}^{2} = 10 \\ c.10[/tex]

Answer:

AC = 10 units .

Step-by-step explanation:

Given  : Triangle  ABC.

To find : What is AC.

Solution : We have given Triangle  ABC.

Triangle BCD is right angle triangle .

By the Pythagorean theorem :

[tex](BC)^{2} = (BD)^{2} + (CD)^{2}[/tex].

Plug the values .

[tex](17)^{2} = (BD)^{2} + (8)^{2}[/tex].

289 =  [tex](BD)^{2} + 64[/tex].

On subtractin g 64 from both sides.

289 - 64 =  [tex](BD)^{2}[/tex].

225  =  [tex](BD)^{2}[/tex].

Taking square root .

BD  = [tex]\sqrt{225}[/tex].

BD  15 units .

AB = AD+ BD

21 = AD + 15

AD = 21 -15

AD = 6 units .

Now , Triangle ACD is right angle triangle .

[tex](AC)^{2} = (6)^{2} + (8)^{2}[/tex].

[tex](AC)^{2} = 36 +64[/tex].

[tex](AC)^{2} =  100[/tex].

Taking square root

AC = 10 units .

Therefore, AC = 10 units .